The Cosine rule

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To solve a triangle is to find the lengths of each of its sides and all its angles.**
**The law of cosines is useful for computing the third side of a triangle when two sides and their enclosed angle are known, and in computing the angles of a triangle if all three sides are known.

The cosine rule is used when we are given either

[a] three sides or

[b] two sides and the included angle.

By changing which sides of the triangle play the roles of *a*, *b*, and *c* in the original formula, the following two formulas also state the law of cosines:

**Skill builder questions
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Practice worksheet – 1 | Cosine rule worksheet – 1 |

Practice worksheet – 2 | Cosine rule worksheet – 2 |

Practice worksheet – 3 | Cosine rule worksheet – 3 |